Boxed out ... Sylvester Stallone received an Oscar for Rocky, so why can't Gary Oldman, seen here in The Contender, get one? Photograph: Snap/Rex Features

It is, no question, shameful that screen legends such as Cary Grant and Greta Garbo, Peter O'Toole and Lauren Bacall have never won a competitive Oscar. But they're trophy magnets compared with the array of great actors who, over the years, were never nominated at all; something even Sylvester Stallone, Oprah and Roberto Benigni all managed (Benigni - pinch yourself - actually won). Here's a tribute to the overlooked and the ignored, suggestions as to why they kept missing the cut and the role(s) that should have bagged them a place on the prestigious final five - at the very least.

The eternal sidekick to his pal Orson Welles, with supporting roles in Citizen Kane and The Magnificent Ambersons. Even when Cotten played the lead, as in The Third Man, Welles insouciantly snaffled the Lime-light. Cotten's low-key style and stolid looks made him strangely easy to underestimate, but he contributed some first-rate performances in a handful of masterpieces. His modern yet refined suitor in Ambersons is a lovely turn but perhaps his best role is as devil-in-suburbia Uncle Charley, aka "The Merry Widow Murderer" in Alfred Hitchcock's Shadow of a Doubt, a charming, chilling villain worthy of a whole mantelpiece of awards, let alone nominations.

Marilyn Monroe – Some Like It Hot (1959); The Misfits (1961)

More worshipped as an idol than admired as an actor, Monroe's sex-bomb image and erratic professionalism practically guaranteed that artistic respect was unlikely. Yet behind the ditzy blonde persona was a young woman – Actors Studio-trained, no less – determined to prove, in films such as Bus Stop or The Misfits, that she could handle drama. And, really, how many "serious actresses" had the comic chops, let alone the matchless blend of smoking sexuality and guileless innocence of her Sugar Kane in Some Like It Hot? It's an iconic role from a genuine actor who just happened to look like a fantasy movie star.

Gary Oldman – The Contender (2000); Sid and Nancy (1986)

Oldman's early, corrosive performances in Alex Cox's Sid and Nancy or Alan Clarke's The Firm were too authentically scuzzy, while later blockbuster bad guys (Air Force One, Leon) were too hammy. But what about the mercurial actor's perfect Oscar-bait roles? An uncanny Lee Harvey Oswald (JFK); an impassioned Beethoven (Immortal Beloved); or his wonderfully oily Republican congressman in political thriller The Contender, where Oldman both chows down on scenery and yet seems more vividly human than his real-life counterpart, Clinton nemesis Ken Starr? Given that his co-stars Joan Allen and Jeff Bridges were voted in by the Academy, we demand a recount for arguably the best actor never Oscar-nominated.

Edward G Robinson – Little Caesar (1931); The Cincinnati Kid (1965)

Squat, pudgy and nasal sounding (he's the inspiration for The Simpsons' Chief Wiggum for heaven's sake), Robinson was nonetheless a fixture in Hollywood's golden age, able to play snarling heavy (Key Largo) or mild-mannered patsy (Scarlet Street). The consummate pro, a nomination for Robinson's elegant supporting turn as a poker legend in The Cincinnati Kid – basically Steve McQueen aping Paul Newman's The Hustler, with cards – would've been an apt career capper. And made amends for the outrageous omission of his venal, brutish gangster in Little Caesar, featuring one of cinema's all-time great exit lines: "Mother of mercy! Is this the end of Rico?"

Donald Sutherland – JFK (1991); Ordinary People (1980)

Is it because he's Canadian? Sutherland, of the mesmeric, buggy eyes and lopsided grin, has starred in enough American classics (M.A.S.H, Klute), propped up countless potboilers and been feted by Europe's finest auteurs – Bertolucci, Fellini et al. Yet Oscar has never once come knocking, even when showering his films and co-stars with trinkets. Scandalously the only thesp of 1980 best picture Ordinary People's leading quartet not nominated – inevitably the only one not indulging in capital-A acting – and unjustly overlooked for his epic 15-plus-minute monologue explaining Oliver Stone's entire JFK, here's one US conspiracy even his Mr X couldn't fathom.

Martin Sheen – Badlands (1973); Apocalypse Now (1979)

Hollywood is usually decried for its liberal outlook, but if that were really so, surely its most ardent, virtuous leftie Sheen would have been invited to its annual rally just once? Long before he won awards and adulation as the US's dream president on TV's The West Wing, it's unthinkable he wasn't rewarded for standout work in two 70s classics. Sheen anchors showboating turns from Brando and Duvall in Apocalypse Now, his commitment nearly killing him in the process; and Badlands' Kit Carruthers is one of the all-time great portraits of alienated youth, a James Dean wannabe as deluded sociopath.

Christopher Plummer – The Insider (1999); Syriana (2005)

Being a Brit and primarily a stage actor didn't stop Olivier racking up Oscar nods but Plummer's, well, plummy tones and theatrical bent might've counted against him, despite actually being, like his pal Sutherland, a Canuck. Difficult to argue for his early leading man roles – The Sound of Music etc – but as an in-demand character actor, Plummer's Academy neglect is baffling. His sly takedown of US TV anchor Mike Wallace in The Insider seemed a lock but somehow missed out, as did sterling support in award-fodder such as A Beautiful Mind and Syriana. Still, two Tony awards presumably offer some consolation.

Mia Farrow – Broadway Danny Rose (1984); Rosemary's Baby (1968)

For female actors, a sure-fire way to get Oscar's attention is to work with Woody Allen. Never mind Diane Keaton and Dianne Wiest, when even Mira Sorvino can triumph and Jennifer Tilly can get nominated, how is it possible that Allen's most frequent onscreen foil never managed a single nomination? True she's usually straight (wo)man to Allen's one-liners (whereas Keaton unearthed equal laughs), but Farrow had eye-catching roles: the tragic movie addict in The Purple Rose of Cairo or her blowsy, tough-talking hooker in Broadway Danny Rose. And arguably she was owed way before Woody, her unwitting demon mother bringing the real terror to Polanski's Rosemary's Baby.

Jeff Goldblum – The Fly (1986); The Big Chill (1983)

The only genre seemingly less respected than comedy, horror films are mongrels at the dog show, whatever their pedigree. David Cronenberg's masterful, if grotesque, body horror parable gave Jeff Goldblum his greatest ever starring role as the scientist who slowly turns insect. But sadly the offbeat actor's nuanced, ultimately heartbreaking work, even in a relatively lean year for lead actors, wasn't enough. There's more to Goldblum than quirk but apparently his gangly physicality or his trademark ... time-lapsed line delivery overrides standout turns such as a superbly sleazy yet self-aware journalist in a key 1980s acting ensemble. Talk about The Big Chill.

Steve Martin – Roxanne (1987); All of Me (1984)

No one in their right mind would push Martin for his recent second-hand, second-rate output – godawful Cheaper By the Dozens and Pink Panthers – but the "wild and crazy guy" who first wowed on stage, TV and film was a genuine original. His genius physical contortions playing a man half-controlled by Lily Tomlin in All Of Me was perhaps too outré for awards. But his double threat, as sophisticated writer and tender star of Roxanne, the Cyrano reimagining, was a dead cert – until typical Academy comedic snobbery won through. Whoever said "dying is easy, comedy is hard" obviously had winning Oscars in mind.